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. 2022 Feb 18;12:2833. doi: 10.1038/s41598-022-06875-4

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Model-predicted log relative risk ratio derived for 13 species-specific effect sizes for retained species. Shrinkage estimates were derived using a precision weighted Bayesian random-effects meta-analytic model with Gaussian likelihood. Polygon = density of the posterior draws (the effective sample size = 10,000) and the horizontal line underneath each polygon = 95% highest posterior density interval (HDI) of the posterior draws, solid dot = mean of the posterior draws shrunk towards the pooled or Random Effect, which is the mean or overall expected log relative risk ratio for all 13 species (right-side labels = the posterior mean and HDI summaries). Below the density polygon is an open dot = observed effect size and thin horizontal line = observed effect size ± 1 standard deviation derived using the metafor::escalc() function. The difference between solid and open dots reflects the degree of shrinkage that is dependent on sample size.